Preheat oven to 350°F. Butter the sides and bottom of a 17 x 12-inch baking sheet, a 17 x 12-inch cake pan (shown in photos), or a very large casserole dish. Set the pan aside.
To a medium non-stick sauce pan, add the butter over medium low heat to begin to melt. As the butter melts, it will begin to foam. Allow the butter to get past the foam stage and while still over medium low heat, turn a nice shade of golden brown. The butter should smell nutty. Remove from the heat.
Away from the heat, to the melted butter add the chopped onion, the whole grain Dijon, and the regular Dijon mustards. Stir to combine. Return to medium low heat and cook for 5 minutes, a little longer if you want to intensify the flavor. I try for 10 minutes if I have the time.
Using a serrated knife, and without separating the individual rolls, slice each package in half horizontally. Assemble the bottom halves of the rolls onto the prepared baking sheet, cutting to make even rows and so all fit.
Use a silicon pastry brush to brush the bottoms with some of the butter mixture. The rolls must not become saturated, rather just brushed with enough of the butter mixture to flavor the slider.
Next, layer the shaved ham and the Swiss cheese and 2 pickle chips per slider. Replace the top halves of the rolls. NOTE if doing double cheese, assemble the first layer of cheese directly atop the bottom halves of the rolls once brushed with the butter mixture. Follow with shaved ham, additional Swiss cheese, and pickle chips. Replace the top halves of the rolls.
Drizzle the remaining butter mixture over the tops of the rolls and use the pastry brush to move the butter and the onions around to coat all the tops and the nooks and crannies. Cover with heavy gauge aluminum foil and bake for 10 minutes. Carefully remove the foil and bake uncovered for an additional 7 to 10 minutes. Tops should be golden but still soft.
Remove from the oven and allow to cool for about 5 minutes before allowing eaters to reach in and pull apart as the freshly baked sliders will be very hot.